Paper

The Cauchy problem for the Pavlov equation9

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Published 30 September 2015 © 2015 IOP Publishing Ltd & London Mathematical Society
, , Citation P G Grinevich et al 2015 Nonlinearity 28 3709 DOI 10.1088/0951-7715/28/11/3709

0951-7715/28/11/3709

Abstract

Commutation of multidimensional vector fields leads to integrable nonlinear dispersionless PDEs that arise in various problems of mathematical physics and have been intensively studied in recent literature. This report aims to solve the scattering and inverse scattering problem for integrable dispersionless PDEs, recently introduced just at a formal level, concentrating on the prototypical example of the Pavlov equation, and to justify an existence theorem for global bounded solutions of the associated Cauchy problem with small data.

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Footnotes

  • An essential part of this work was made during the visit of the three authors to the Centro Internacional de Ciencias in Cuernavaca, Mexico in November–December 2012.

10.1088/0951-7715/28/11/3709